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Offline Bill Spight
 Post subject: Subtle sente problem
Post #1 Posted: Wed Dec 08, 2010 1:21 pm 
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Click Here To Show Diagram Code
[go]$$W White to play. Which sente?
$$ --------------------
$$ | . O X . X O O . . .
$$ | . O X X X X O . . .
$$ | . O a . W X O . . .
$$ | . O b , . X O . O ,
$$ | . O X X X X X O . .
$$ | . O O X O . O X O .
$$ | . . X O X X . X O .
$$ | . . O O O X . X O .
$$ | . . . . . . . . . .[/go]


There are no kos on the board, nor will there be a future ko. The time has come for White to play sente at "a" or "b". Under these conditions, one play dominates the other. That is, it will sometimes be better, and will never be worse. Which sente should White play?

Enjoy! :)

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.
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Offline emeraldemon
 Post subject: Re: Subtle sente problem
Post #2 Posted: Wed Dec 08, 2010 1:35 pm 
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Ok, I'll try :)

This looks like a job for a difference game (http://senseis.xmp.net/?DifferenceGame)
Click Here To Show Diagram Code
[go]$$ Position at move 1
$$ ---------------------------------------
$$ | . O X . . . . . . O X . . . . . . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . O O . O X O X . . X . . . . . . . . |
$$ | . O . , . X O . . X X . . . . , . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]


If black goes first:
Click Here To Show Diagram Code
[go]$$Bcm1 Black plays first
$$ ---------------------------------------
$$ | . O X . . . . . . O X . . . . . . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . O O 1 O X O X 2 . X . . . . . . . . |
$$ | . O 3 , . X O . 4 X X . . . . , . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]


Black gets an extra point. But if white goes first:

Click Here To Show Diagram Code
[go]$$Wcm1 Position at move 1
$$ ---------------------------------------
$$ | . O X . . . . . . O X . . . . . . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . O O 2 O X O X 1 . X . . . . . . . . |
$$ | . O 3 4 . X O . 5 X X . . . . , . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]



It's a draw. So it seems like the correct play is black's knight approach, because it creates the option for an extra point.
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Offline hyperpape
 Post subject: Re: Subtle sente problem
Post #3 Posted: Wed Dec 08, 2010 1:47 pm 
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Click Here To Show Diagram Code
[go]$$W White to play. Which sente?
$$ --------------------
$$ | . O X . X O O . . .
$$ | . O X X X X O . . .
$$ | . O . a W X O . . .
$$ | . O 1 , . X O . O ,
$$ | . O X X X X X O . .
$$ | . O O X O . O X O .
$$ | . . X O X X . X O .
$$ | . . O O O X . X O .
$$ | . . . . . . . . . .[/go]


Click Here To Show Diagram Code
[go]$$W
$$ --------------------
$$ | . O X . X O O . . .
$$ | . O X X X X O . . .
$$ | . O 1 a W X O . . .
$$ | . O . , . X O . O ,
$$ | . O X X X X X O . .
$$ | . O O X O . O X O .
$$ | . . X O X X . X O .
$$ | . . O O O X . X O .
$$ | . . . . . . . . . .[/go]


If Black plays a in both diagrams, he is clearly better in the second.

Looked at your solution, emeraldemon. Difference games look complicated.

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Offline Magicwand
 Post subject: Re: Subtle sente problem
Post #4 Posted: Wed Dec 08, 2010 2:02 pm 
Tengen
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Click Here To Show Diagram Code
[go]$$W White to play. Which sente?
$$ --------------------
$$ | . O X . X O O . . .
$$ | . O X X X X O . . .
$$ | . O a . W X O . . .
$$ | . O b , . X O . O ,
$$ | . O X X X X X O . .
$$ | . O O X O . O X O .
$$ | . . X O X X . X O .
$$ | . . O O O X . X O .
$$ | . . . . . . . . . .[/go]


ok i guess this is for kyu level players...but i will give you my answer.
b is always better than a.
Click Here To Show Diagram Code
[go]$$W black will have 3 point in that area
$$ --------------------
$$ | . O X . X O O . . .
$$ | . O X X X X O . . .
$$ | . O 3 4 W X O . . .
$$ | . O 1 2 . X O . O ,
$$ | . O X X X X X O . .
$$ | . O O X O . O X O .
$$ | . . X O X X . X O .
$$ | . . O O O X . X O .
$$ | . . . . . . . . . .[/go]


Click Here To Show Diagram Code
[go]$$W black has 3 points same as above.
$$ --------------------
$$ | . O X . X O O . . .
$$ | . O X X X X O . . .
$$ | . O 1 2 W X O . . .
$$ | . O 3 4 . X O . O ,
$$ | . O X X X X X O . .
$$ | . O O X O . O X O .
$$ | . . X O X X . X O .
$$ | . . O O O X . X O .
$$ | . . . . . . . . . .[/go]



now second diag black can tenuki and only lose 1 point.
first diag black have to answer because he will lose 3 point.

first diag will take away tenuki of black so it is always better.

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Offline Bill Spight
 Post subject: Re: Subtle sente problem
Post #5 Posted: Fri Dec 10, 2010 1:01 pm 
Honinbo

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Well, everybody got the right answer, but only Magicwand gets full credit. :)

Difference games give the solutions to problems like this. You mirror the board to make an even positon and then let each player play one of the options. If the result is better for one player, that player's move is dominant. (Kos defeat this procedure, which is the reason for the caveat.)

Click Here To Show Diagram Code
[go]$$Bcm1 Black plays first
$$ ---------------------------------------
$$ | . O X . . X O . . O X . . . . . . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . O W 1 O X O X 4 3 X . . . . . . . . |
$$ | . O 5 , . X O . 2 B X . . . . , . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]


emeraldemon got the right answer, but White's reply in the difference game is wrong. This is the correct sequence.

Click Here To Show Diagram Code
[go]$$Wcm1 White plays first
$$ ---------------------------------------
$$ | . O X . . X O . . O X . . . . . . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . O W 4 O X O X 3 2 X . . . . . . . . |
$$ | . O 5 6 . X O . 1 B X . . . . , . . . |
$$ | . O X X X X O O O O X . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]



Black to play wins, while White to play can only get jigo. So Black's original play (marked) is dominant.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.


Last edited by Bill Spight on Fri Dec 10, 2010 1:56 pm, edited 4 times in total.
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Offline Bill Spight
 Post subject: Re: Subtle sente problem
Post #6 Posted: Fri Dec 10, 2010 1:09 pm 
Honinbo

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Never mind. ;) See next. :)

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.


Last edited by Bill Spight on Fri Dec 10, 2010 1:22 pm, edited 2 times in total.
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Offline Bill Spight
 Post subject: Re: Subtle sente problem
Post #7 Posted: Fri Dec 10, 2010 1:14 pm 
Honinbo

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Well, if one play is dominant, it should be easy to construct a board where it wins and the other play does not. I have sort of done that here. (I ask you to imagine parts of the board that are not in play, however. ;))


_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

This post by Bill Spight was liked by: Li Kao
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